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Least k > n^2 such that (k^3+1)/(n^2+1) is an integer.
0

%I #15 Apr 06 2020 08:04:31

%S 3,9,19,33,43,48,99,69,163,201,197,289,339,393,451,513,579,374,411,

%T 801,543,644,1059,791,725,1353,739,1244,863,1801,1063,2049,1699,1245,

%U 1905,1663,2739,2889,3043,3201,3363,3529,2099,2383,4051,2783,3059,4609,2973,3525

%N Least k > n^2 such that (k^3+1)/(n^2+1) is an integer.

%F a(n) = 2*n^2 + 1 for n = 1, 2, 3, 4, 7, 9, 10, 12, 13, 14, 15, 16, 17, 20, 23, 26, ...

%o (PARI) a(n) = {my(d=n^2+1); for(k=d, oo, if((k^3+1)%d==0, return(k))); } \\ _Jinyuan Wang_, Apr 05 2020

%K nonn

%O 1,1

%A _Benoit Cloitre_, Jan 04 2002

%E Name clarified and more terms from _Jinyuan Wang_, Apr 05 2020